Lock ‘Em Up

Charles Murray writes:

Here is a graph that shows the violent crime rate per 100,000 population and the number of prisoners per 1,000 violent offenses from 1960–2010:

Source: Bureau of Justice Statistics, FBI Uniform Crime Reports. “Prisoners” refers to inmates of state and federal prisons and does not include persons in jail.


When crime gets safer, crime goes up very quickly as a response. In the late 1950s, the “prison only makes people into smarter criminals”  school became dominant in criminal justice circles. By the early 1960s, imprisonment rates were plummeting. For that matter, even the raw number of prisoners fell. One consequence was that every cohort of young people saw acquaintances start to get probation for offenses that would have sent them to prison or reform school in the 1950s. I still remember my shock as a 17-year-old in that era when a friend of mine who shoplifted several thousand dollars of clothes from the store where he worked got probation. Once he had been arrested, it had not occurred to me that he wouldn’t go to reform school.

Pushing that toothpaste back into the tube takes a lot longer. Kids who are amazed when a friend gets away with a serious crime aren’t amazed when, say, 19 percent of their friends arrested for a serious crime are incarcerated instead of 15 percent. Understandably, crime continued to rise after imprisonment rates started to rise after 1974. Even in 1990, after 15 years of rising imprisonment rates, the risk of going to prison if you committed a violent crime was still far lower than it had been in 1960.

Cumulatively, however, two things happen. First, more and more of the “dirty 7 percent” of offenders who commit about 50 percent of all crime end up in prison. They cannot commit crimes, except against other criminals. Second, the cumulative impact of much higher imprisonment rates does make an impression—the idea that crime doesn’t pay is no longer completely a joke. For violent crime, the tipping point occurred in 1992, when imprisonment rates were heading straight up. By the time that the imprisonment rate for violent crime reached its 1960 level in 1998, the downward trendline was well established.

So how much of the reduction in violent crime was produced by increased incarceration? This kind of analysis doesn’t tell us…. (“Keep locking ’em up,” The Enterprise Blog, December 29, 2011)

I assessed the effect of imprisonment on the crime rate in a post that is now more than four years old. The following material is excerpted from that post.

I … considered as explanatory variables the existence of mandatory federal sentencing guidelines (1989-2004), number of male enlisted personnel in the armed forces (in proportion to population), and year-over-year growth in real GDP per capita — in addition to the number of persons aged 15-24, number of prisoners, and number of blacks in proportion to total population, as before. (For sources, see the footnote to this post.) Here’s a graphical depiction of the crime rates and all of the variables I considered:

Key: VIC, violent crimes per 100,000 persons; VPC, violent+property+crimes per 100,000 persons; BLK, blacks as a proportion of population; ENL (active-duty, male, enlisted personnel as a proportion of population aged 15-24; GRO(C), growth of real GDP per capita as a proxy for year-to-year growth (GRO) used in the regression analysis; PRS, prisoners in federal and State penitentiaries as a proportion of population; SNT, mandatory sentencing guidelines in effect (0 = no, 1 = yes); YNG, persons aged 15-24 as a proportion of population.

A few comments about each of the explanatory variables: BLK, unfortunately, stands for a segment of the population that has more than its share of criminals — and victims. Having more men in the armed forces (ENL) should reduce, to some extent, the number of crime-prone men in the civilian population. (It would also help to alleviate our self-inflicted impotence, by putting more “boots on the ground” — and missiles in readiness.) I use the annual rate of real, per-capita economic growth (GRO) to capture the rate of employment — or unemployment — and the return on employment, namely, income. (The use of year-over-year growth vice cumulative growth avoids collinearity with the other variables.) PRS encompasses not only the effects of taking criminals off the streets, but the means by which that is done: (a) government spending on criminal justice and (b) juries’ and courts’ willingness to put criminals behind bars and keep them there for a good while. SNT ensures that convicted criminals are put away for a good while.

I focused on violent-plus-property crime (VPC) as the dependent variable, for two reasons. First, there is a lot more property crime than violent crime (VIC); that is, VPC is a truer measure of the degree to which crime affects Americans. Second, exploratory regression runs on VPC yielded more robust results than those on VIC.

Even at that, it is not easy to tease meaningful regressions from the data, given high correlations among several of the variables (e.g., mandatory sentencing guidelines and prison population, number of blacks and prison population, male enlistees and number of blacks). The set of six explanatory variables — taken one, two, three, four, five, and six at a time — can be used to construct 63 different equations. I estimated all 63, and rejected all of those that returned coefficients with counterintuitive signs (e.g., negative on BLK, positive on GRO).

Of the 63 equations, I chose the one that has the greatest number of explanatory variables, where the sign on every explanatory variable is intuitively correct, and — given that — also has the greatest explanatory power (as measured by its R-squared):

VPC (violent+property crimes per 100,000 persons) =


+346837BLK (number of blacks as a decimal fraction of the population)

-3040.46GRO (previous year’s change in real GDP per capita, as a decimal fraction of the base)

-1474741PRS (the number of inmates in federal and State prisons in December of the previous year, as a decimal fraction of the previous year’s population)

The t-statistics on the intercept and coefficients are 19.017, 21.564, 1.210, and 17.253, respectively; the adjusted R-squared is 0.923; the standard error of the estimate/mean value of VPC = 0.076.

The minimum, maximum, and mean values of the dependent and explanatory variables:

VPC: 1887, 5950, 4773 (violent-plus-property crimes/100,000 persons)

BLK: 0.1052, 0.1300, 0.1183 (blacks/population)

GRO: -0.02866, 0.06263, 0.02248 (growth in real GDP per capita during year n-1/real GDP per capita in year n-2)

PRS: 0.0009363, 0.004842, 0.002243 (federal and State prisoners in December of year n-1/average population in year n-1)

Even though the coefficient on GRO isn’t strongly significant, it isn’t negligible, and the sign is right — as are the signs on BLK and PRS. The sign on the intercept is counterintuitive — the baseline rate of crime could not be negative. The negative sign indicates the omission of key variables. But forcing variables into a regression causes some of them to have counterintuitive signs when they are highly correlated with other, included variables.

In any event, the equation specified above does a good job of explaining variations in the crime rate:

I especially like the fact that the equation accounts for two policy-related variables: GRO and PRS:

1. Crime can be reduced if economic growth is encouraged by rolling back tax rates. Crime will rise if growth is inhibited by raising tax rates (even for the very rich).

2. Crime can be reduced by increasing the rate at which it is prosecuted successfully, and by ensuring that prisoners do not receive lenient sentences….

ENL and YNG, like SNT, are key determinants of the crime rate. Each of the three variables appears, with the right sign, in many of the 63 equations. So, I am certainly not ruling out ENL and YNG as important variables. To the contrary, they are important variables. But, just as with SNT, I can’t satisfactorily quantify their importance because of the limitations of regression analysis.

Crime, then, depends mainly on two uncontrollable variables (BLK and YNG), and four controllable ones: ENL, GRO, PRS, and SNT. The controllable variables are salutary means of reducing crime, and the record shows that they work….

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